Write the coordinates of the vertices after a reflection over the x-axis.

Answer:

comparing given quadratic equation x²-5x-4=0 with ax²+bx+c=0 we get,

a=1,b=-5,c=-4

Now,

x={-b±√b²-4ac}/2a

={-(-5)±√(-5)²-4×1×-4}/2×1

={5±√25+16}/2

=(5±√41)/2

Hence,B.is the correct option

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The value of the proportion x is 10. When determining if two ratios or fractions are equivalent, the proportion formula is utilized.

When determining if two ratios or fractions are equivalent, the proportion formula is utilized. By dividing the supplied numbers, we may determine the missing value. One way to express the percentage formula is as a: Whereas a and d are the extreme terms and b and c are the mean terms, b::c: d = a/b = c/d.

1)Cross, multiply, and spread

2) Be sure to alter the signs when you move the x to one side and the numbers without the x to the other.

3)solve

4)x=

x - 2 /4 = x + 4 /2

2x-4 = 4x+ 16

-20= 2x

x=10.

The value of the proportion x is 10.

The complete question is

Solve the proportion : x - 2 /4 = x + 4 /2

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The expression a² + b⁴ - 7a³ - a² + b⁴ - 7a³ is a binomial.

Degree of the binomial = 4.

A polynomial is defined as an expression which is composed of variables, constants and exponents, that are combined using mathematical operations such as addition, subtraction, multiplication and division (No division operation by a variable).

The degree of a polynomial is the highest power of the variable in a polynomial expression.

Given expression

a² + b⁴ - 7a³ - a² + b⁴ - 7a³

Combining like terms

2b⁴ - 14a³

above expression has where a and b as variables with power 4 and 3 and coefficients 2 and 14 respectively combined with subtraction operation.

So, it is a polynomial with two terms which means it is a binomial and its degree is 4.

Hence, the expression a² + b⁴ - 7a³ - a² + b⁴ - 7a³ is a binomial with degree 4.

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The gradient of the line in the image will be -3.

Slope or the gradient is the number or the ratio which determines the direction or the steepness of the line. The slope of the line is defined as the ratio of the rise of the line to the run of the line.

Given that the line in the image is passing through the points ( 0,3) and (1,0). the gradient or slope of the line will be calculated as:-

Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )

Slope = ( 0 - 3 0 / 9 1 - 0 )

Slope = -3

Hence, the gradient will be -3.

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Answer:

slope 2/5

y-intercept (0,2)

Step-by-step explanation:

The coordinates of point A are ( 5/4, -3/4)

What are coordinates?

A pair of numbers that use the separations between the two reference axes to define the location of a point on a coordinate plane. usually represented by the x- and y-values, respectively, (x, y).

The position of a point or a shape in a given space is determined by coordinates, which are numbers (a map or a graph ).

x - coordinate = 5 grid lines to the right of the y-axis

y - coordinate =   3 grid lines below the x-axis.

The point A is in the 4th quadrant

(x,y) = ( + 5 grid lines, -3  grid lines )

There are increments I have one over four for each grid line on each of the two axes

This means,

(x,y) = ( + 5 * 1/4, -3*1/4 ) = ( 5/4, -3/4)

So,  the coordinates of point A are ( 5/4, -3/4)

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The bearing form the cliff to the island is 58.09 degrees

Information from the question

A puffin leaves a cliff and flies 33 km due east

and then 53 km due north

Work out the bearing form the cliff to the island = ?

The bearing form the cliff to the island is worked using SOH CAH TOA

Sin = opposite / hypotenuse - SOH

Cos = adjacent / hypotenuse - CAH

Tan = opposite / adjacent - TOA

The direction of movements describes a right triangle of

opposite = 53 km

adjacent = 33 km

The bearing is calculated using tan, TOA

let the angle be x

tan x = Opposite / Adjacent

tan x = 53 / 33

tan x = 1.60606

x = arc tan 1.60606

x = 58.09 degrees

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The slope of the line shown below is -5/8.

Slope is the measure of the steepness or incline of a line or surface. It is calculated by measuring the ratio of the vertical change over the horizontal change between two points. It is a mathematical concept used in algebra, geometry, and calculus to measure the rate of change of a function or line. Slope is also used to identify the direction of a line or surface. It is represented by the variable ‘m’ and is calculated by dividing the vertical change by the horizontal change between any two points on a line or surface.

This can be determined by using the formula for slope, which is (y2 - y1)/(x2 - x1). In this equation,

(y2 - y1) = -3 - 2 = -5 and (x2 - x1) = -2 - 6 = -8. Thus, the slope of the line is -5/8.

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The equation of the function is found to be y = [tex]2^{2x+3}[/tex].

What is a function?

A unique kind of relation called a function is one in which each input has precisely one output. In other words, the function produces exactly one value for each input value. The graphic above shows a relation rather than a function because one is mapped to two different values. The relation above would turn into a function, though, if one were instead mapped to a single value. Additionally, output values can be equal to input values.

The x-values are input into the function machine. The function machine then performs its operations and outputs the y-values. The function within can be any function.

y = 2⁽ᵃˣ⁺ᵇ)

x = - 1     y  = 2 = 2¹

=> ax + b = 1   =>  -a  + b = 1

=> b  -a  = 1

x = 0     y  = 8 = 2³

=> ax + b = 3   =>  0  + b = 3

=> b   =  3

b -a  = 1

=> 3  - a  = 1

=> a = 2

checking for others

x  = 1    y  = 32 = 2⁵

ax + b = 2(1)  +  3  = 5

x = 2    y = 128  = 2⁷

ax + b = 2(2) + 3 = 7

The equation is y = [tex]2^{2x+3}[/tex]

Hence the equation of the function is found to be y = [tex]2^{2x+3}[/tex].

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Religion is an example of a variable measured at the nominal level of measurement. Thus, option B is correct.

Nominal values are those that cannot be quantified by numbers, such as when calculating age or tallying academic accomplishments. As opposed to the ordinal, interval, or ratio measurements, it is the level of measurement representing a variable that just has distinct properties.

Since the 'characteristic' or 'identity' we are interested in is just named, the nominal level of measurement is the least accurate and illuminating. In nominal variables, the numerical values just "label" the attribute in a distinctive way. The numerical value is just a label in this instance.

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The resistance of 19.0m of the given copper pipe is 1.19 x [tex]10^{-6}[/tex] ohm.

The resistance of a pipe is given by the formula:

R = (p * L) / (A * n)

where R is the resistance, p is the resistivity of the material (in this case, copper), L is the length of the pipe, A is the cross-sectional area of the pipe, and n is the number of conductors (in this case, 1).

To find the cross-sectional area of the pipe, we first need to find the radius of the pipe. We can do this by taking the difference between the outside diameter and the inside diameter and dividing by 2:

r = (d_outside - d_inside) / 2

r = (5.00 cm - 3.00 cm) / 2

r = 1.00 cm

Now we can find the cross-sectional area of the pipe:

A = pi * [tex]r^2[/tex]

A = pi * [tex](1.00 cm)^2[/tex]

A = 3.14

Next, we can use the resistivity of copper, which is 1.68 x[tex]10^{-8}[/tex] ohm-cm. Now we have all the values required to find the resistance of the pipe:

R = (p * L) / (A * n)

R = (1.68 x [tex]10^{-8}[/tex] ohm-cm * 19.0 m) / (3.14 [tex]cm^2[/tex] * 1)

R = (1.68 x [tex]10^{-8}[/tex] ohm-cm * 19.0 m) / (3.14 [tex]cm^2[/tex])

R= 1.19 * [tex]10^{-6}[/tex] ohm

Therefore, the resistance of 19.0m of this pipe is 1.19 x [tex]10^{-6}[/tex] ohm.

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Answer:

y=x-5000

Step-by-step explanation:

Given,

total sum of money mom has=x

money spent on grocery=Rs 3000

money spent on milk= Rs 2000

total money spent by mom=Rs 5000

Let the money left with the mom =y

then the algebric expression for the amount left with her is given by

y=x-5000

the function f(x)=10^x and ploted below.

What is a function?

A unique kind of relation called a function is one in which each input has precisely one output. In other words, the function produces exactly one value for each input value. The graphic above shows a relation rather than a function because one is mapped to two different values. The relation above would turn into a function, though, if one were instead mapped to a single value. Additionally, output values can be equal to input values.

The x-values are input into the function machine. The function machine then performs its operations and outputs the y-values. The function within can be any function.

function f(x)=10^x

Y = 0

Y greater than 0

(0,1)

Decreases toward 0

Hence, the function f(x)=10^x and plotted below.

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Y = 12.12 cm is determined by Pythagoras' Theorem, where the hypotenuse and one side of a right-angled triangle are specified as being 14 cm and 7 cm, respectively.

Triangles are shapes with three sides and three vertices, making them polygons. It is one of geometry's fundamental forms. A triangle containing vertices A, B, and C is known as a triangle ABC. In Euclidean geometry, a singular plane and triangle are discovered when the three points are not collinear. A polygon with three sides and three corners is called a triangle. The corners of the triangle are the points where the three sides meet one another end to end.

given

by Pythagoras theorem

c2 = a2 + b2

14*14 = y2 + 7*7

196 - 49 = y2

y2 = 147

y = [tex]\sqrt{147}[/tex]  = 12.12 cm

Y = 12.12 cm is determined by Pythagoras' Theorem, where the hypotenuse and one side of a right-angled triangle are specified as being 14 cm and 7 cm, respectively.

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Bank A will give better return for the money we invest. The solution has been obtained using the concept of compound interest.

What is compound interest?

The interest earned on savings that is computed using both the original principal and the interest accrued over time is known as compound interest.

It differs from simple interest in that simple interest does not take the principal into account when calculating the interest for the following month. In math, compound interest is typically represented by the letter C.I.

We have 2 different financial institutions which suit our investment needs.

1. Bank A offering an interest rate of 8.8% compounded quarterly.

2. Bank B offering an interest rate of 9.0% compounded annually.

In order to find that which bank will give better return of our money, we need to calculate the effective rate of interest for both the options.

1. 8.8% compounded quarterly

Effective interest= (1+(0.088/4))^4-1

= (1.022)^4-1

= 1.09094-1

= 0.09094

= 9.094%

2. 9.0% compounded annually

Effective interest= (1+(0.09/1))^1-1

= 1.09-1

= 0.09

= 9%

Hence, Bank A will give better return for the money we invest.

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Answer:

2x+1<9

collecting the like term

2x<9-1

2x<8

divide both sides by 2

x<4

Answer:keep dividing

Step-by-step explanation:

keep dividing till you get a common factor

When asked which of the following is true in this situation, "if a distribution has zero variants," the response is "D."

Due to the variance's definition, which is the same for both continuous and discrete random variables, all of the values must be equal to one another. For all possible values of X, the variance is determined by measuring the excess distance from the mean.

If any one of these individual values deviates from the mean, it follows that the variations must also deviate from zero because the integration will result in the difference squared being represented as a positive number.

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Therefore , the solution to the given problem of function comes out to be slant asymptotes are y = x -4.

Numbers and their variants, equations & related structures, and geometry and their regions and potential applications are all mathematical topics. The link between a group of input, each of which generates a related output, is referred to as a "function." A function is a relationship between outputs and inputs where each input results in a single, distinct output. Each procedure has a domain and a city / municipality, which are frequently referred to as a scope. Functions are usually represented by the letter f. (x). The input is X. On activity, one-to-one activities, many-to-one activities, throughout operations, as well as on functions are the four main categories of supplied functions.

Here,

There are no limitations on the type of rational function, therefore it is feasible to construct one with each of the three asymptotes.

This is depicted in the attached graph, along with the graph of the rational function it represents. These are the asymptotes of the function.

Vertical asymptotes are x = -4,

horizontal asymptotes are y = 0 and

slant asymptotes are y = x -4.

Additional remarks

We employ an exponential function in our example function. Although it can be expressed as a polynomial of infinite degree, that is not often regarded as a polynomial. The proportion of polynomials is how most authors describe a rational function.

Therefore , the solution to the given problem of function comes out to be slant asymptotes are y = x -4.

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Remaining two data of Theo's observation is 9 and 11.

Mean is the average of all data value. Range is the difference between the highest and lowest value of a data set. Median implies the middle value of a data set. If the number of data is even than median is calculated from average of two middle value. If the number of data is odd, then the median is the middle of all data.

given, Kendra and Theo both collected data of bird observation.

Kendra data's summary are as following.

range = 6

median = 7

mean = 7

From the Theo's data

range = 6

median = 7

mean = 7.5

the question shows 6 data among the total 8 data of Theo's observation.

5,5,6,6,8,10 are 6 data of total 8 data.

let, the missing value are X and Y.

we know mean of a data list is calculated by adding all the value and divided the sum by total amount of data.

mean = 7.5 = (X + Y + 5+ 5+ 6+ 6+ 8+10) / 8

             X + Y + 40 = 60

                               X+Y = 20

we know range is the difference between the highest and the lowest number of a data set.

let, the highest number is X and lowest number is assumed 5.

As range is 6, range = X - 5

                          X- 5 = 6

                     X = 11

 highest number of data set = 11

now we get the other missing data from the equation, X + Y = 20

                                                          Y = 20 -11

                                                     Y = 9

now, the data set can be arranged as

5,5,6,6, 8,9, 10,11

we notice that the two middle value is 6 and 8.

median = (6+8) / 2 = 7

that is equal to given median by Theo.

hence, the determination is verified.

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The value of a in the equation 8 = 3a - 4 is

A linear equation is an algebraic equation of the form y=mx+b. involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept. Occasionally, the above is called a "linear equation of two variables," where y and x are the variables.

The equation 8 = 3a -4 is an example of linear equation with only one variable. The variable here is a. And the value of this variable can be found using mathematics principle.

8 = 3a - 4

collect like terms

3a = 12

divide both sides by 3

a = 12/3

a = 4

therefore the value of a in 8 = 3a -4 is 4

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Answer: It would take the ostrich 4 minutes

Step-by-step explanation:

The time taken by the Ostrich running at a rate of 50 miles in 60 minutes to cover a distance of 15 miles is 18 minutes.

Speed is simply referred to as distance traveled per unit time.

Mathematically, Speed = Distance ÷ time.

Given the data in the question;

An ostrich can run at a rate of 50 miles in 60 minutes.

First, we determine the speed of the ostrich.

Speed = Distance / time

Speed = 50 / 60

Speed = 5/6 miles per min

Now, time taken for the ostrich to run 15 miles will be;

Speed = Distance / time

Time = Distance ÷ Speed

Time = 15 ÷ 5/6

Time = 15 × 6/5

Time = 3 × 6

Time = 18 min

Therefore, the time taken by the Ostrich is 18 minutes.

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a. g(3) = -2

b. g is increasing and concave down on the intervals (-3 <= x < 2) and (2 <= x <= 4).

c.  h'(3) = 0

d. The slope of the tangent line to the graph of p at x = -1 is -3.

a. The function g is defined as the definite integral of f(t) with respect to t from -3 to 2. Therefore, g(3) = integral_2^3 f(t) dt. From the graph, we can see that:

Therefore, g(3) = integral_2^3 (-t) dt + integral_2^3 (2t - 8) dt

= -1/2(3^2 - 2^2) + 1/2(3^2 - 2^2 - 8(3 - 2)) = -5/2 + 1/2 = -2.

b. The graph of g is increasing and concave down when the graph of f is concave down and when the definite integral of f is increasing. From the graph of f, we can see that f is concave down on the intervals (-5 <= t < -3) and (2 <= t <= 4). Therefore, g is increasing and concave down on the intervals (-3 <= x < 2) and (2 <= x <= 4).

c. The function h is defined by h(x) = g(x)/5x. To find h'(3), we need to use the quotient rule for derivatives. h'(x) = (5xg'(x) - g(x)5)/5x^2.

Since g(x) = integral_2_-3 f(t) dt, it is not a function of x, so g'(x) = 0. Therefore, h'(3) = (530 - 05)/53^2 = 0.

d. The function p is defined by p(x) = f(x^2 - x). To find the slope of the line tangent to the graph of p at the point where x = -1, we need to find the derivative of p at -1. Using chain rule: p'(x) = f'(x^2-x)(2x-1) so p'(-1) = f'(-1) * (2(-1)-1) = (2(-1) -1) = -3.

Therefore, the slope of the tangent line to the graph of p at x = -1 is -3.

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Answer: Let's say Trisha is currently T years old and Mina is currently M years old.

We know from the problem statement that Trisha is twice as old as Mina:

T = 2M

We also know that 10 years from now, Trisha will be 4 years older than Mina:

T + 10 = M + 4

We can substitute the first equation into the second equation:

2M + 10 = M + 4

We can then solve for M:

M = 6

So, Mina is currently 6 years old.

We can use the first equation to find Trisha's current age:

T = 2M = 2 * 6 = 12

Therefore, Trisha is currently 12 years old and Mina is currently 6 years old.

Step-by-step explanation:

Damian should put 5 shelves in the display case to hold 75 model cars and ensure that each shelf has the same number of cars.

What is the unit value?

Unit value is a measure of the price of a single unit of a good or service. It is calculated by dividing the total cost of the good or service by the number of units purchased. It is also known as unit cost.

To determine how many shelves Damian should put in the display case, we can use the following steps:

Divide the total number of cars by the maximum number of cars per shelf. In this case, 75 model cars / 15 cars per shelf = 5

If the number of shelves is not a whole number, round up to the next whole number. In this case, 5 shelves is already a whole number, so we don't need to round up.

Check that the number of shelves is less than 10. In this case, 5 shelves are less than 10 shelves.

Hence, Damian should put 5 shelves in the display case to hold 75 model cars and ensure that each shelf has the same number of cars.

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Answer:

a) Balph can lose a maximum of 6 times in a row before running out of money and not being able to place any more bets. This is because if he loses 6 times in a row, he would have to bet $64 (1+2+4+8+16+32) which is more than the $31 he has in his wallet.

b) The probability that Balph wins a dollar is 0.9596 and the probability that he loses everything is 0.0404. These probabilities are calculated by assuming a 18/38 probability of winning each bet and using the martingale betting strategy.

c) The expected value of Balph's net winnings from one martingale is -$0.29236. This means that on average, Balph can expect to lose $0.29236 each time he plays the martingale betting strategy.

d) The possible values for the total amount wagered are $1, $3, $7, $15, $31, and $64. These values correspond to the amount wagered after losing 0, 1, 2, 3, 4 and 5 times in a row. The probability of each value depends on the probability of losing that many times in a row, calculated using the 18/38 probability of winning each bet. The expected value of the number of dollars wagered is $5.55475.

e) The amount Balph wins per dollar bet is -0.0527. This number is calculated by dividing the expected value of Balph's net winnings by the expected value of the number of dollars wagered. This number is less than zero, indicating that on average, Balph will lose money for every dollar he bets.

In this equation, the value of x in the ratio 4x-1/ 3x + 7 = 6/5 is 23.5.  In algebra, an equation is a mathematical statement .

A mathematical formula known as an equation combines two assertions using the equal sign (=) to denote equivalence. An equation is a mathematical statement that proves the equality of two mathematical expressions, according to the definition of an equation in algebra. The terms 3x + 5 and 14 are separated by an equal sign in the equation 3x + 5 = 14, for example. Mathematical equations are used to express the relationship between two phrases on either side of a letter. In most cases, the symbol serves as the sole variable.

given

4x-1/ 3x + 7 = 6/5

20x - 5 = 18x + 42

x = 23.5

In this equation, the value of x in the ratio 4x-1/ 3x + 7 = 6/5 is 23.5.

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The linear function to find average cost will be A=$(2.25+0.079t), average cost of a comic book in 2020 = $4.3, Average cost will be $5 in year 2029.

what is a linear function?

A linear function is a function which forms a straight line in a graph. It is generally a polynomial function whose degree is utmost 1 or 0.  Although the linear functions are also represented in terms of calculus as well as linear algebra. The only difference is the function notation. Knowing an ordered pair written in function notation is necessary too. f(a) is called a function, where a is an independent variable in which the function is dependent. Linear Function Graph has a straight line whose expression or formula is given by;

                                                    y = f(x) = px + q

It has one independent and one dependent variable. The independent variable is x and the dependent one is y. P is the constant term or the y-intercept and is also the value of the dependent variable. When x = 0, q is the coefficient of the independent variable known as slope which gives the rate of change of the dependent variable.

Now

Initial value = $2.25 in 1994

cost in 2016 = $3.99

Therefore

3.99=2.25+2.25*r*22/100

r=0.079

where r=rate

then

Average cost=initial value+0.079t

Hence

A=$(2.25+0.079t)

where t=time (given year - 1994)

cost in 2020=$(2.25+0.079*26)

cost in 2020=$4.3

Now for A=$5

5=2.25+0.079t

t=35years

Hence Average cost will be $5 in year 2029.

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The answer is 4/5

Probability is a measure of the likelihood of an event occurring. The probability formula is defined as the possibility of an event happening is equal to the ratio of the number of favorable outcomes and the total number of outcomes. Probability of event to happen P(E) = Number of favorable outcomes/Total Number of outcomes.

Given here: Mitch  won 12 matches and lost 3 matches.

Thus the theoretical probability of him winning the next match is 12/15=4/5

Hence, The answer is 4/5

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Answer:

Step-by-step explanation:

yes

no

no

ye